where \(x\)  denotes the location of the cell and \(c(x)\)  is the concentration of the attractant at that location, \(m\)  stands for the methylation level of the dimer which can take any integer value between 0 and 8 [1]}, [2]}, [3]}, [4]} and \(\epsilon _0\)  and \(\epsilon _1\)  are two constants whose values are listed in Table REF . The parameters \(K_{min}\)  and \(K_{max}\)  set the range of sensitivity, i.e. the cell can sense any concentration as long as \(K_{min} < c(x) < K_{max}\)  is satisfied. A receptor cluster of size \(n\)  contains \(3n\)  dimers, where the factor 3 accounts for the formation of trimer of dimers. The total free energy of the cluster is the sum of individual free energies of all \(3n\)  dimers
\(F = 3n \log \frac{1+c(x)/K_{min}}{1+c(x)/K_{max}} +3n \epsilon _0 - \sum _{i=1} ^{3n} \epsilon _1 m(i)\) 
